Find the points of local maxima or local minima and corresponding local maximum and local minimum values of each of the following functions. Also, find the points of inflection, if any:
f(x) = x3 – 2ax2 + a2 x, a > 0, x ∈ R
local maximum value = f(4)
= 4√(32 – 42)
= 4√(32 – 16)
= 4√16
= 16
Local minimum at x = – 4
Local minimum value = f(– 4)
= – 4√(32 – (– 4)2)
= – 4√(32 – 16)
= – 4√16
= – 16
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